I had a similar diagnosis, and was advised to take 6-8 weeks rest from running and start back with a beginners running schedule. In the meantime, I did other training (as long as it didn’t feel painful) such as swimming, cycling, cross-trainer and Bodypump (weights classes including squats, lunges) and core work, together with yoga. I also started taking Osteocare calcium and vitamin D tablets.
The bad news is that it takes a while to recover, and the return to running (1 min walk, 1 min run x 3) seemed worse than not running at all; the good news is I’ve fully recovered and have run marathons in the two years since.
So the proper advice would be to work on everything you can whilst not running and then build up gradually when you can run again, which means ruling out London. Would your sponsors donate for you doing a different marathon later in the year?
If you must have a go at the London there would seem little point in trying a long run before marathon day, better to risk it on the day rather than in training.